Abstract

Occupation-time derivatives are complex barrier-type options where valuation
depends on the time spent beyond the barrier by the underlying asset. This thesis
presents a model for corporate bonds using an occupation-time derivative, the
ParAsian option, the features of which can capture bankruptcy resolution and complex
capital structure with violations of the absolute priority rule. It investigates the
numerics of the problem, and proposes appropriate numerical techniques to enable
accurate and rapid solutions. The model is extended to include bond conversion in
a two-tier structure, which presents its own numerical problems. A new occupationtime
derivative that takes into account the distance of deviations beyond the barrier
is presented and solved.
Using existing knowledge on the asymptotic structure, new fast and efficient techniques
are created for pricing American options. A second new occupation-time
derivative is proposed, combining elements of early exercise with the ParAsian option
to produce the American delayed-exercise option.
The numerical methods employed in this thesis are based on accurate finitedifference
schemes, specifically developed and enhanced to treat the various classes
of problem considered.